A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball (0809.3402v3)

Abstract: Using the AdS/CFT correspondence, we calculate a fermionic spectral function in a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the $AdS_4$ background with a charged black hole. The spectral function shows no quasiparticle peak but the Fermi surface is still well defined. Interestingly, all momentum points inside the Fermi surface are critical and the gapless modes are defined in a {\it critical Fermi ball} in the momentum space.

• The paper demonstrates that the fermionic spectral function from a charged black hole lacks a quasiparticle peak while retaining a clear Fermi surface.
• By solving the Dirac equation in the black hole background, the study uncovers a 'critical Fermi ball' where all interior momentum points exhibit gapless modes.
• These findings offer new insights into unconventional electronic phases and advance the use of AdS/CFT in modeling strongly correlated materials.

Overview of "A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball"

The paper presented by Sung-Sik Lee utilizes the framework of the AdS/CFT correspondence to explore the dynamics of a unique non-Fermi liquid state in a 2+1 dimensional quantum field theory. The focal point of the paper is a fermionic spectral function derived from a corresponding gravitational setup involving a charged black hole in an asymptotically $AdS_4$ space.

Key Findings

The computation reveals a notable absence of a quasiparticle peak within the spectral function, a characteristic aspect that marks a deviation from traditional Fermi liquid behavior. Nevertheless, the Fermi surface remains discernible. The intriguing result is the emergence of what the author refers to as a "critical Fermi ball." Within this momentum space, all points inside the Fermi surface are deemed critical, featuring gapless modes. This observation challenges the usual paradigm wherein only excitations at the Fermi surface are gapless in quantum liquids.

By solving the Dirac equation in the charged black hole background, the paper exposes the presence of an algebraic singularity in the spectral function at zero energy for momenta beneath a specific threshold. This critical momentum, denoted as $k_c$, signifies the extent of the critical Fermi ball and aligns with the boundary where the broad peak edges converge with the Fermi energy. The zero-energy peak's existence over a two-dimensional disk contrasts with conventional non-Fermi liquid systems characterized by singular behavior solely near the Fermi surface.

Implications

The implications of the research are multifold, touching both theoretical and practical aspects. The findings, especially the notion of a critical Fermi ball, hint at novel strongly correlated electronic phases that could manifest in various condensed matter systems. Understanding these unconventional states could prove vital in comprehending the complexities of strongly correlated materials, such as high-temperature superconductors and heavy fermion compounds.

From a theoretical vantage, the work furthers the bridge between gravitational theories and condensed matter phenomena via AdS/CFT duality. It underscores the utility of gravitational frameworks to model and predict enigmatic quantum field behaviors under strong interaction conditions. Such frameworks may offer insights or lead to the development of comprehensive theories addressing states beyond the Fermi liquid paradigm.

Speculation on Future Developments

Future research could explore the broader implications of a critical Fermi ball through detailed investigations into instabilities, as well as thermodynamic and transport properties of these quantum states. Potential studies may also delve into the structure of the critical Fermi ball and its stability against perturbations, both in theoretical models and experimental setups. Additionally, considering finite temperature effects, as briefly touched on in the paper could elucidate how thermal fluctuations shape the dynamics of non-Fermi liquid states.

Furthermore, building nuances into the existing gravitational description to capture a wider array of materials or phase transitions could be a promising direction. This endeavor could pave the way to discern distinct characteristics of higher-dimensional correspondences influencing lower-dimensional quantum field theories.

In essence, the paper anchors a significant advancement in understanding non-Fermi liquids, posing relevant questions and setting clear objectives for future exploratory pathways in quantum physics. Through insights offered by the AdS/CFT perspective, it enriches the dialogue on high-energy physics' relevance in condensed matter systems.